The classical problem of quantizing an analog signal into some set of a-priori chosen discrete-alphabet values, was extensively studied following the pioneering work of Shannon on rate distortion theory published in 1948 by C. E. Shannon, "A mathematical theory of communication" Bell System Technical Journal, 27, 1948.
Various quantization methods are known to those skilled in the art. In general, each of these methods utilizes a specific cost function. The object of a quantlzer is to minimize the respective quantization cost.
In digital communication applications, digital information is modulated onto a carrier signal which is then, transmitted over an analog channel. The output of the channel is sampled, quantized and processed by the receiver in order to recover the transmitted digital information.
The natural cost function which is used in this case is the probability of error. The objective of the quantization strategy is to minimize the probability of incorrectly receiving the transmitted information.
Unfortunately, analytically minimizing this cost function is mathematically intractable even for relatively simple scenarios (see e.g. Salz and Zehavi). Accordingly, ad-hock solutions are often used.
Reference is now made to FIG. 1, which is a schematic illustration of a digital communication receiver, generally referenced 10, known in the art.
System 10 includes an analog to digital (A/D) converter 12, a demodulator 14, an automatic-gain-control (AGC) unit 15, a quantizer 16, and a decoder 18.
The transmitted signal is picked-up by the receivers antenna and is then amplified and filtered at the receiver's front-end (not shown in FIG. 1). The resulting signal is fed into system 10 at the input of the A/D 12.
The A/D 12 converts the signal to digital samples and provides them to the demodulator 14. The demodulator 14 processes the digitized samples and produces a demodulated signal Y[n]. The AGC unit 15 normalizes the demodulated signal Y[n], to fit into the dynamic range of the quantizer 16, as follows EQU Y[n]=AGC.sub.-- Gain.multidot.Y[n] Equaton 1
where AGC.sub.-- Gain may vary from sample to sample. PA1 where S[n] is the desired (information bearing) signal that needs to be decoded, h is the complex valued channel gain, and W[n] is an additive white Gaussian noise term. PA1 detecting the fading characteristics of the fading channel, and PA1 determining a quantization correction command for at least one segment of the received signal.
The quantizer 16 processes the normalized samples Y[n], thereby producing the quantized samples Q(Y[n]) such that each sample is represented by B bits. In most cases, Q(Y[n]) is simply the nearest element to Y[n] in the set of 2.sup.B possible quantization levels. The quantized samples are provided to the decoder 17, which in turn attempts to recover the transmitted information.
It is noted that system 10 is a mere example to systems which are known in the art. Those skilled in the art are familiar with several other configurations. For example, in a spread-spectrum CDMA (Code Division Multiple Access) environment operating on a multi-path fading channel, the demodulator is replaced by a rake demodulator. A rake demodulator includes a plurality of demodulating fingers, each of which attempts to detect and demodulate a different replica of the transmitted signal.
According to another example, an analog demodulator may be utilized. In this case, an A/D converter is placed after the demodulator, sometimes also serving as a quantizer.
However, regardless of the specific receiver type and structure, its complexity, or more particularly, the complexity of the decoder, increases with B--the number of bits used to represent each quantized sample Q(Y[n]). Therefore, it is desirable to choose a quantization strategy that minimizes B.
The minimal possible value for B is B=1, which is called "Hard Decision". In this case the numbers produced by the quantizer are restricted to have only two possible values "one" and "zero". All other situations are called "Soft Decision" and correspond to the case where B&gt;1.
When hard-decision is used, only the sign of Y[n] is fed into the decoder, thus completely ignoring any information conveyed by its magnitude. Therefore, hard-decision decoding, although very simple to implement, can lead to a significant degradation in performance.
On the other hand, when B is very large, the full potential of the code is utilized. It will be noted however, that in this case, the decoder complexity is high. It is therefore desirable to come-up with an efficient quantization strategy that allows good tradeoff between decoder complexity and quantization loss.
Methods for quantizing the input to a soft decoder operating over a static AWGN channel are described in Onyszchuk et. al. In this case, the demodulated signal can be represented by EQU Y[n]=h.multidot.S[n]+W[n] Equation 2
The conventional quantization strategy for such channels is based on first normalizing the RMS (Root Mean Square) value of Y[n] to a predetermined vague denoted by Desired.sub.-- RMS, and then applying a uniform quantizer e.g. a conventional A/D converter. The normalization operation is performed by the AGC according to Equation 1, by setting ##EQU1## where the Estimated.sub.-- RMS may be computed in a variety of ways, e.g. ##EQU2##
This quantization strategy performs well when the channel is static, (i.e. the model in Equation 2 holds).
However, when implemented for non-static channels, this approach can lead to a significant degradation in performance. In order to clarify this, we now consider a simple generalization of Equation 2, in which EQU Y[n]=h[n].multidot.S[n]+W[n] Equation 5
where, as before, Y[n] is the demodulated signal; S[n] is the information bearing signal; W[n] is the additive white Gaussian noise term; and h[n] is the complex valued channel gain which is now allowed to be time varying.
Reference is now made to FIGS. 2A, 2B, 2C and 2D.
FIG. 2A is an illustration of a frame of a transmitted signal, generally referenced 140A. The signal is divided into a plurality of sections 150A, 152A, 154A, 156A, 158A and 160A, each including a plurality of symbols represented by dots. For example, section 150A includes five symbols. The first three symbols and the fifth symbol, are of a value of +1, while the fourth symbol is of a value of -1.
FIG. 2B is an illustration of a dynamically fading channel where we plotted only its magnitude .vertline.h[n].vertline., generally referenced 142. Each of the dots along the line represents the gain of the channel at a point in time which is respective to a symbol of signal 140A (FIG. 2A).
FIG. 2C is an illustration of the demodulated signal Y[n] of the received frame in the absence of noise according to the simple model of Equation 5, generally referenced 140B. Each of the samples in the demodulated signal 140B is, in general, a multiplication of a selected transmitted symbol of signal 140A (FIG. 2A) and the respective fading value of the channel 142 (FIG. 25).
FIG. 2D is an illustration of the quantized signal Q(Y[n]), produced from signal 140B, when AGC.sub.-- Gain is set to unity and the following five level uniform quantizer utilized, ##EQU3##